Download Right Angle Trig Apps

Key Steps in Trigonometry Applications
1) Draw a picture of the problem, if a drawing is not included in the original problem.
2) Find right-triangle(s) inherent and useful to the problem. If you can only find non-right triangles perhaps there
are similar triangles to work with. Perhaps you can cut a non-right triangle into two right triangles.
2) Label the triangle(s). Label both known and unknown sides and angles.
3) Determine which relation(s) is relevant.
4) Set up an appropriate equation with one unknown measurement.
5) Solve the equation to determine the missing measurement.
6) Repeat as necessary until all measurements are determined or the original question has been answered
Problem 1
Find the height of the flag pole.
Problem 2
Find the length of the guy wire.
Problem 3
Find the plane's elevation in feet.
Problem 4
Find the plane's angle of descent.
Problem 5
700' into a tunnel, an air shaft must be
drilled so as to reach the surface 635'
uphill from where the tunnel starts. For
optimum efficiency, the air shaft must
take the shortest route to the surface.
At what angle will the shaft intersect
the tunnel? Note: the shortest route will
intersect the surface at 90°. Why?
Problem 6
Find the angle a 22' ladder makes with
the ground if its base is set 6' 9" from
the wall.
With more complex geometries, the triangles are not necessarily so obvious. The crucial task is to try to fit right-triangles
into the geometry. Of course, there are other relationships to consider as well such as the Pythagorean Theorem, similar
triangles, arc lengths, complementary angles and so on. Use only Right Triangle Trigonometry
Problem 7
Marc is standing 160 feet from a tall
building. From there, he measures the
angle (from the horizontal) to the top of
the building at 38.4°. There is a flag
pole on the edge of the roof. Marc
measures the angle to the top of the flag
pole too. That angle measures 44.2°.
What is the length of the flag pole?
Problem 8
While Lydia is walking toward a tall
Clock Tower she measures the angle
(from the horizontal) to the clock at
34.6°. After she moves 25 m closer,
she measures the angle again. It now
measures 46.2°. How high is the clock
above the ground?
Problem 9
(a) Find the equation for the line (in
slope-intercept
form)
which
crosses the y-axis at (0, 6) at an
angle of -24.2°. That is, the line
is angled downward.
(b)
Find the x-intercept.
Problem 10
A satellite is tracked from two stations
that are 1,400 statute miles apart on the
Earth. At the point that the satellite is
exactly midway between the stations,
the "line of sight" to the satellite is
offset 72° 18' 48" from directly
overhead. How high is the satellite's
orbit above the Earth? Earth radius ≈
3,960 mi.
Problem 11
A trapezoid window has a width of 4', a
height of 4' and the interior angle of 70°
(a)
Find its area.
(b)
Find its perimeter.
w = 4', h1 + h2 = 4'
Problem 13
A hi-way bridge spans 140'. The underside is formed with a circular
arc. The sides are canted inward at 74°. The bridge is 12' thick in the
center and 24' (diagonally) along the sides. Find the bridge's crosssectional area.
Problem 14
A 10 ft vertical retaining wall is built at the base of a hill
which has a 68% grade. The area behind the wall is to be
filled so that the final grade slopes from the retaining wall
back towards the hill at an 8° down-slope. How much fill
(cu-yds) is required for each foot of length of the retaining
wall?
h1 + h2 = 10'
Problem 15
A scissor truss is made by joining a number of
components. Find the cutting angles θ1, & θ2 for a scissor
truss with a top rafter @ 7 ½ / 12 pitch and a bottom rafter
@ 3/12 pitch.
Problem 12
A telephone pole is located 165' down a
main street. Perpendicular to that main
street is a side street. 140' down that
side street a sighting is taken to the top
of the pole @ 22.5°. How tall is the
pole?
Problem 16
A driver is going up a road sloped at 12% which eventually flattens out. A 4' tall child is playing in the road 50' from the
edge of the slope. The driver's eyes are 5' above the road bed when the vehicle is on flat ground. At what point will the
driver begin to see the child?
There are two situations we explore in working with geographic distances. The first is applications in which the Earth's
surface should be treated as a curved surface with an average radius of roughly 3960 mi. The second is applications where
the distances are small enough so that the curvature of the Earth is negligible and the Earth's surface can be treated as flat.
Problem 17
(a) Find the conversion from one degree latitude to surface miles. This is constant
throughout Earth.
(b)
Find the conversion (at θ° latitude) from one degree longitude to surface miles.
This varies with latitude.
RE ≈ 3,960 mi, RE ≈ 6,370 km
Problem 18
A Ship at sea has a lookout in the crows nest 20 m above the water looking for a lighthouse that is situated on a rock
outcropping. The light of the lighthouse is 45 m above the water. At what distance will the lookout see the light directly?
RE ≈ 3,960 mi, RE ≈ 6,370 km
The next 3 Problems assume all distances are small enough so that the Earth's curvature is negligible.
Problem 19
A map shows Madras @ 44° 43' N, 121° 12' W, Redmond @ 44° 15' N, 121° 12' W and Sisters @ 44° 15' N, 121° 40' W.
What is the straight-line distance between (a) Redmond and Madras, (b) Redmond and Sisters (c) Sisters and Madras.
Problem 20
Valerie needs to calculate the distance across the Crooked River Gorge so her
company can build a bridge for a movie set. As she looks across the gorge she
spots a tree on the other side directly across from where she is standing. Her
compass gives a reading of 20° azi (aka N 20° E) toward the tree. Valerie turns
clockwise 90° (so she is looking up the gorge) and walks 200 feet along the rim of
the gorge. At that point, she takes a second compass reading toward the same
tree. That reading is 344.5° azi (N 15.5° W). How wide is the gorge to the
nearest foot?
Problem 21
A tank travels 1,000 yds from pt A to pt B on a N 30° E bearing and then changes
direction and travels due east 1,200 yds from pt B to pt C. What direction and how
far must the tank travel to return to its starting point most directly?